First, note that science is not a monolithic entity. Second, technically speaking, the role of statistical certainty in using models to determine what constitutes reality is the heart of a primary metaphysical debate in the philosophy of science: realism vs. instrumentalism. The most prominent example of this in practical science is in quantum physics and controversy around the acceptance of the Copenhagen interpretation.
Your question goes to a very important metaphysical debate in the philosophy of science, that of the underdetermination of scientific theory (SEP). When one starts throwing around the adverb 'really', what one is doing is presuming dualism: that is to say, that there are physical and mental "worlds" and they do not relate. Cartesian duality is the most famous dualistic theory, and many philosophers reject it outright, like material eliminativists such as Daniel Dennett.
From SEP above:
So a high correlation between cartoon viewing and violent playground behavior is evidence that (by itself) simply underdetermines what we should believe about the causal relationship between the two. But it turns out that this simple and familiar predicament only scratches the surface of the various ways in which problems of underdetermination can arise in the course of scientific investigation.
So, instead of determinism and indeterminism in the context of bivalued logics-- something is either deterministic or indeterministic-- statistical models often attempt to determine to what degree something is deterministic, like in the notion of correlation. If you presume that a statistical model is mental and is not absolutely a certain measure of the physical, then you wind up with ideas like the classic phrase: correlation does not imply causation. And if statistical measures are, given a degree of unpredictability or randomness inherent in their nature, not causal strictly speaking, then it actually begs the question, is there a reality at all or is our thought nothing but models, and relatedly, can we really know a thing-in-itself?